Derivation of eigenvectors for spatial processing in MIMO communication systems

ABSTRACT

Techniques for deriving eigenvectors based on steered reference and used for spatial processing. A steered reference is a pilot transmission on one eigenmode of a MIMO channel per symbol period using a steering vector for that eigenmode. The steered reference is used to estimate both a matrix Σ of singular values and a matrix U of left eigenvectors of a channel response matrix H. A matrix Ũ with orthogonalized columns may be derived based on the estimates of Σ and U, e.g., using QR factorization, minimum square error computation, or polar decomposition. The estimates of Σ and U (or the estimate of Σ and the matrix Ũ) may be used for matched filtering of data transmission received via a first link. The estimate of U or the matrix Ũ may also be used for spatial processing of data transmission on a second link (for reciprocal first and second links).

CLAIM OF PRIORITY UNDER 35 U.S.C. § 119

The present Application for Patent claims priority to ProvisionalApplication No. 60/432,760 entitled “Derivation of Eigenvectors forSpatial Processing in MIMO Communication Systems” filed Dec. 11, 2002,and assigned to the assignee hereof and hereby expressly incorporated byreference herein.

BACKGROUND

I. Field

The present invention relates generally to data communication, and morespecifically to techniques for deriving eigenvectors based on steeredreference and used for spatial processing in multiple-inputmultiple-output (MIMO) communication systems.

II. Background

A MIMO system employs multiple (N_(T)) transmit antennas and multiple(N_(R)) receive antennas for data transmission. A MIMO channel formed bythe N_(T) transmit and N_(R) receive antennas may be decomposed intoN_(S) independent or spatial channels, where N_(S)≦min{N_(T), N_(R))}.Each of the N_(S) independent channels corresponds to a dimension. TheMIMO system can provide improved performance (e.g., increasedtransmission capacity and/or greater reliability) if the additionaldimensionalities created by the multiple transmit and receive antennasare effectively utilized.

In a wireless communication system, data to be transmitted is typicallyprocessed (e.g., coded and modulated) and then upconverted onto a radiofrequency (RF) carrier signal to generate an RF modulated signal that ismore suitable for transmission over a wireless channel. For a wirelessMIMO system, up to N_(T) RF modulated signals may be generated andtransmitted simultaneously from the N_(T) transmit antennas. Thetransmitted RF modulated signals may reach the N_(R) receive antennasvia a number of propagation paths in the wireless channel. Thecharacteristics of the propagation paths typically vary over time due tovarious factors such as, for example, fading, multipath, and externalinterference. Consequently, the RF modulated signals may experiencedifferent channel conditions (e.g., different fading and multipatheffects) and may be associated with different complex gains andsignal-to-noise ratios (SNRs).

To achieve high performance, it is often necessary to estimate theresponse of the wireless channel between the transmitter and thereceiver. For a MINO system, the channel response may be characterizedby a channel response matrix H, which includes N_(T)N_(R) complex gainvalues for N_(T)N_(R) different transmit/receive antenna pairs (i.e.,one complex gain for each of the N_(T) transmit antennas and each of theN_(R) receive antennas). Channel estimation is normally performed bytransmitting a pilot (i.e., a reference signal) from the transmitter tothe receiver. The pilot is typically generated based on known pilotsymbols and processed in a known manner (i.e., known a priori by thereceiver). The receiver can then estimate the channel gains as the ratioof the received pilot symbols over the known pilot symbols.

The channel response estimate may be needed by the transmitter toperform spatial processing for data transmission. The channel responseestimate may also be needed by the receiver to perform spatialprocessing (or matched filtering) on the received signals to recover thetransmitted data. Spatial processing needs to be performed by thereceiver and is typically also performed by the transmitter to utilizethe N_(S) independent channels of the MIMO channel.

For a MIMO system, a relatively large amount of system resources may beneeded to transmit the pilot from the N_(T) transmit antennas such thata sufficiently accurate estimate of the channel response can be obtainedby the receiver in the presence of noise and interference. Moreover,extensive computation is normally needed to process the channel gains toobtain eigenvectors needed for spatial processing. In particular, thereceiver is typically required to process the channel gains to derive afirst set of eigenvectors used for spatial processing for data receptionon one link and may further be required to derive a second set ofeigenvectors used for spatial processing for data transmission on theother link. The derivation of the eigenvectors and the spatialprocessing for data transmission and reception are described below. Thesecond set of eigenvectors typically needs to be sent back to thetransmitter for its use. As can be seen, a large amount of resources maybe needed to support spatial processing at the transmitter and receiver.

There is therefore a need in the art for techniques to more efficientlyderive eigenvectors used for spatial processing in MIMO systems.

SUMMARY

Techniques are provided herein for deriving eigenvectors based onsteered reference and used for spatial processing for data reception andtransmission. A steered reference is a pilot transmission on only onespatial channel or eigenmode of a MIMO channel for a given symbolperiod, which is achieved by performing spatial processing with asteering vector for that eigenmode, as described below. The steeredreference is used by a receiver to derive estimates of both a diagonalmatrix Σ of singular values and a unitary matrix U of left eigenvectorsof the channel response matrix H, without having to estimate the MIMOchannel response or perform singular value decomposition of H.

The estimates of Σ and U may be used for matched filtering of datatransmission received via a first link (e.g., the uplink). For a timedivision duplex (TDD) system, which is characterized by downlink anduplink channel responses that are reciprocal of one another, theestimate of U may also be used for spatial processing of datatransmission on a second link (e.g., the downlink).

In another aspect, a matrix Ũ with orthogonal columns is derived basedon the estimates of Σ and U. The orthogonalization of the columns of Ũmay be achieved by various techniques such as QR factorization, minimumsquare error computation, and polar decomposition, all of which aredescribed below. An orthogonal matched filter matrix {tilde over (M)}may then be derived based on the matrix Ũ and the estimate of Σ. Thematrix {tilde over (M)} may be used for matched filtering for the firstlink, and the matrix Ũ may be used for spatial processing for the secondlink.

Various aspects and embodiments of the invention are described infurther detail below.

BRIEF DESCRIPTION OF THE DRAWINGS

The features, nature, and advantages of the present invention willbecome more apparent from the detailed description set forth below whentaken in conjunction with the drawings in which like referencecharacters identify correspondingly throughout and wherein:

FIG. 1 shows a flow diagram of a process for deriving an orthogonalmatched filter matrix {tilde over (M)} based on a steered reference;

FIG. 2 shows a wireless communication system;

FIG. 3 shows a frame structure for a TDD MIMO-OFDM system;

FIG. 4 shows transmission of steered reference and data on the downlinkand uplink for an exemplary transmission scheme;

FIG. 5 shows a block diagram of an access point and a user terminal; and

FIG. 6 shows a block diagram of the spatial processing performed by theaccess point and user terminal for data transmission on the downlink anduplink.

DETAILED DESCRIPTION

The word “exemplary” is used herein to mean “serving as an example,instance, or illustration.” Any embodiment or design described herein as“exemplary” is not necessarily to be construed as preferred oradvantageous over other embodiments or designs.

The techniques described herein for deriving eigenvectors may be usedfor various MIMO communication systems. For example, these techniquesmay be used for single-carrier MIMO systems as well as multi-carrierMIMO systems. For clarity, these techniques are described below for asingle-carrier MIMO system.

The model for a single-carrier MIMO system may be expressed as:r=Hx+n ,  Eq(1)where

-   -   x is a “transmit” vector with N_(T) entries for the symbols sent        from the N_(T) transmit antennas (i.e., x=[x₁ x₂ . . . x_(N)        _(T) ]^(T));    -   r is a “receive” vector with N_(R) entries for the symbols        received via the N_(R) receive antennas (i.e., r=[r₁ r₂ . . .        r_(N) _(R) ]^(T));    -   H is an (N_(R)×N_(T)) channel response matrix;    -   n is a vector of additive white Gaussian noise (AWGN); and        “^(T)” denotes the transpose.        The noise vector n is assumed to have components with zero mean        and a covariance matrix of Λ_(n)=σ²I, where I is the identity        matrix and σ² is the noise variance.

The channel response matrix H may be expressed as:

$\begin{matrix}{{\underset{\_}{H} = \begin{bmatrix}h_{1,1} & h_{1,2} & \ldots & h_{1,N_{T}} \\h_{2,1} & h_{2,2} & \ldots & h_{2,N_{T}} \\\vdots & \vdots & ⋰ & \vdots \\h_{N_{R},1} & h_{N_{R},2} & \ldots & h_{N_{R},N_{T}}\end{bmatrix}},} & {{Eq}\mspace{20mu}(2)}\end{matrix}$where entry h_(i,j), for i∈{1 . . . N_(R)} and j∈{1 . . . N_(T)}, is thecoupling (i.e., complex gain) between the j-th transmit antenna and thei-th receive antenna. For simplicity, the channel response is assumed tobe flat across the entire system bandwidth, and the channel response foreach transmit/receive antenna pair can be represented by a singlecomplex value h_(i,j). Also for simplicity, the following descriptionassumes that N_(R)≧N_(T), the channel response matrix H has full rank,and N_(S)=N_(T)≦N_(R).

The channel response matrix H may be “diagonalized” to obtain the N_(T)independent channels, which are also referred to as spatial channels oreigenmodes. This diagonalization may be achieved by performing eithersingular value decomposition of the channel response matrix H oreigenvalue decomposition of the correlation matrix of H, which is H^(H)H, where “^(H)” denotes the conjugate transpose. For clarity, singularvalue decomposition is used for the following description.

The singular value decomposition of the channel response matrix H may beexpressed as:H=UΣV^(H),  Eq(3)where

-   -   U is an (N_(R)×N_(R)) unitary matrix whose columns are left        eigenvectors of H;    -   Σ is an (N_(R)×N_(T)) diagonal matrix of singular values of H,        which is Σ=diag(σ_(1,1)σ_(2,2) . . . σ_(N) _(T) _(,N) _(T) );        and    -   V is an (N_(T)×N_(T)) unitary matrix whose columns are right        eigenvectors of H.        A unitary matrix M is characterized by the property M^(H)M=I,        which means that the columns of the unitary matrix are        orthogonal to one another and the rows of the matrix are also        orthogonal to one another. The columns of the matrix V are also        referred to as steering vectors. Singular value decomposition is        described in further detail by Gilbert Strang in a book entitled        “Linear Algebra and Its Applications,” Second Edition, Academic        Press, 1980.

Spatial processing may be performed by both the transmitter and thereceiver to transmit data on the N_(T) spatial channels of the MIMOchannel. The spatial processing at the transmitter may be expressed as:x=Vs,  Eq(4)where s is a “data” vector with up to N_(T) non-zero entries for datasymbols to be transmitted on the N_(T) spatial channels. The transmitvector x is further processed and then transmitted over the MIMO channelto the receiver.

The received transmission at the receiver may be expressed as:r=Hx+n=HVs+n=UΣV ^(H) Vs+n=UΣs+n,  Eq(5)where all the terms are defined above.

The spatial processing at the receiver to recover the data vector s maybe expressed as:ŝ=GMr=GΣ ^(T) U ^(H) r=GΣ ^(T) U ^(H)(UΣs+n)=s+ñ,  Eq(6)where s is the data vector;

-   -   ŝ is an estimate of the data vector s;    -   M is an (N_(T)×N_(R)) matched filter matrix, which is M=Σ        ^(T)U^(H);    -   G is an (N_(T)×N_(T)) scaling matrix, which is G=diag(1/σ_(1,1)        ² 1/σ_(2,2) ² . . . 1/σ_(N) _(T) _(,N) _(T) ²); and    -   {circumflex over (n)} is the post-processed noise, which is        {circumflex over (n)}=GΣ^(T)U^(H)n.        The spatial processing by the receiver is often referred to as        matched filtering. Since M=Σ^(T)U^(H) and since the columns of U        are left eigenvectors of H. the columns of M^(T) are conjugated        left eigenvectors of H scaled by the singular values in Σ.

As shown in equation (6), the receiver needs good estimates of thematrices Σ and U in order to perform the matched filtering to recoverthe data vector s. The matrices Σ and U may be obtained by transmittinga pilot from the transmitter to the receiver. The receiver can thenestimate the channel response matrix H based on the received pilot andperform the singular value decomposition of this estimate, as shown inequation (3), to obtain the matrices Σ and U. However, as noted above, alarge amount of resources may be needed to transmit this pilot and toperform the singular value decomposition.

I. Steered Reference

In an aspect, a steered reference is transmitted by the transmitter andused by the receiver to derive estimates of the matrices Σ and U, whichare needed for matched filtering. The steered reference is a pilottransmission on only one spatial channel or eigenmode for a given symbolperiod, which is achieved by performing spatial processing with asteering vector for that eigenmode. The receiver can then estimate thematrices Σ and U based on the steered reference, without having toestimate the MINO channel response or perform the singular valuedecomposition.

A steered reference sent by the transmitter may be expressed as:x _(sr,m) =v _(m) ·p, for m∈{1 . . . N _(T)},  Eq(7)where

-   -   x_(sr,m) is the transmit vector for the steered reference for        the m-th eigenmode;    -   v_(m) is the right eigenvector of H for the m-th eigenmode; and    -   p is a pilot symbol transmitted for the steered reference.        The eigenvector v_(m) is the m-th column of the matrix V, where        V=[v₁ v₂ . . . v_(N) _(T) ].

The received steered reference at the receiver may be expressed as:r _(sr,m) =Hx _(sr,m) +n=Hv _(m) p+n=UΣV ^(H) v _(m) p+n=u _(m)σ_(m)p+n,  Eq(8)where

-   -   r_(sr,m) is the receive vector for the steered reference for the        m-th eigenmode; and    -   σ_(m) is the singular value for the m-th eigenmode.

As shown in equation (8), at the receiver, the received steeredreference in the absence of noise is equal to u_(m)σ_(m)p, which is theknown pilot symbol p transformed by u_(m)σ_(m). The eigenvector u_(m) isthe m-th column of the matrix U, and the singular value σ_(m) is them-th diagonal element of the matrix Σ. The receiver can thus obtain anestimate of u_(m)σ_(m) based on the steered reference sent by thetransmitter.

Various techniques may be used to process the received steered referenceto obtain estimates of u_(m) and σ_(m). In one embodiment, to obtain anestimate of u_(m)σ_(m), the receive vector r_(sr,m) for the steeredreference sent on the m-th eigenmode is first multiplied with thecomplex conjugate of the pilot symbol, p*. The result may then beintegrated over multiple steered reference symbols received for eacheigenmode m to obtain the estimate of u_(m)σ_(m). A row vector{circumflex over (m)}_(m) may be defined to be equal to the conjugatetranspose of the estimate of u_(m)σ_(m) (i.e., {circumflex over(m)}_(m)={circumflex over (σ)}_(m)û_(m) ^(H)). Each of the N_(R) entriesof the vector {circumflex over (m)}_(m) is obtained based on acorresponding one of the N_(R) entries of the vector r_(sr,m).

The row vector {circumflex over (m)}_(m) for the m-th eigenmode includesestimates of both u_(m) and σ_(m), and may thus be referred to as ascaled vector. Since eigenvectors have unit power, the singular valueσ_(m) may be estimated based on the received power of the steeredreference, which can be measured for each eigenmode. In particular, thesingular value estimate {circumflex over (σ)}_(m) may be set equal tothe square root of the power for the vector r_(sr,m), divided by themagnitude of the pilot symbol p. The vector {circumflex over (m)}_(m)may be scaled by 1/{circumflex over (σ)}_(m) to obtain the eigenvectorû_(m).

In another embodiment, a minimum mean square error (MMSE) technique isused to obtain an estimate of u_(m) based on the receive vector r_(sr,m)for the steered reference. Since the pilot symbol p is known, thereceiver can derive an estimate of u_(m) such that the mean square errorbetween the recovered pilot symbol {circumflex over (p)} (which isobtained after performing matched filtering on the receive vectorr_(sr,m)) and the transmitted pilot symbol p is minimized.

The steered reference is transmitted for one eigenmode at a time (i.e.,one eigenmode for each symbol period of steered reference transmission).The steered reference for all N_(T) eigenmodes may be transmitted invarious manners. In one embodiment, the steered reference is transmittedfor one eigenmode for each frame, where a frame is an interval of datatransmission for the system and is defined to be of a particular timeduration (e.g., 2 msec). For this embodiment, the steered reference formultiple eigenmodes may be transmitted in multiple frames. In anotherembodiment, the steered reference is transmitted for multiple eigenmodeswithin one frame. This may be achieved by cycling through the N_(T)eigenmodes in N_(T) symbol periods. For both embodiments, the n-thsteered reference symbol may be expressed as:x _(sr,m)(n)=v _([n mod N) _(T) _(]+1) ·p, for n∈{1 . . . L},  Eq(9)where n is an index for either symbol period or frame number and L isthe number of steered reference symbols to be transmitted. Multiplesteered reference symbols may be transmitted for each eigenmode m toallow the receiver to obtain more accurate estimate of u_(m)σ_(m).

The receiver is able to obtain the row vector {circumflex over (m)}_(m)for each of the N_(T) eigenmodes based on the received steered referencefor that eigenmode. The row vectors {circumflex over (m)}_(m) for allN_(T) eigenmodes may be used to form an initial matched filter matrix{circumflex over (M)}, where {circumflex over (M)}=[{circumflex over(m)}₁ {circumflex over (m)}₂ . . . {circumflex over (m)}_(N) _(T) ]^(T)and {circumflex over (M)}={circumflex over (Σ)}^(T)Û^(H). The matrix{circumflex over (M)} may be used for matched filtering by the receiver,as shown in equation (6), to recover the transmitted data vector s.

The steered reference is sent for one eigenmode at a time and may beused by the receiver to obtain the matched filter vector {circumflexover (m)}_(m) for that eigenmode. Since the N_(T) matched filter vectors{circumflex over (m)}_(m) of the matrix {circumflex over (M)} areobtained individually and over different symbol periods, and due tonoise and other sources of degradation in the wireless channel, theN_(T) vectors {circumflex over (m)}_(m) of the matrix {circumflex over(M)} are not likely to be orthogonal to one another. If the N_(T)vectors {circumflex over (m)}_(m) are thereafter used for matchedfiltering of a received data transmission, then any errors inorthogonality among these vectors would result in cross-talk between theindividual symbol streams sent on the N_(T) eigenmodes. The cross-talkmay degrade performance.

II. Eigenvector Orthogonalization

In another aspect, to improve performance, an enhanced matched filtermatrix {tilde over (M)} is derived based on the steered reference andhas row vectors that are forced to be orthogonal to one other. Theorthogonalization of the row vectors of {tilde over (M)} may be achievedby various techniques such as QR factorization, minimum square errorcomputation, and polar decomposition. All of these orthogonalizationtechniques are described in detail below. Other orthogonalizationtechniques may also be used and are within the scope of the invention.

1. QR Factorization

QR factorization decomposes the transposed initial matched filtermatrix, {circumflex over (M)}^(T), into an orthogonal matrix Q_(F) andan upper triangle matrix R_(F). The matrix Q_(F) forms an orthogonalbasis for the columns of the matrix {circumflex over (M)}^(T) (i.e., therows of {circumflex over (M)}), and the diagonal elements of the matrixR_(F) give the length of the components of the columns of {circumflexover (M)}^(T) in the directions of the respective columns of Q_(F). Thematrices Q_(F) and R_(F) may be used to derive an enhanced matchedfilter matrix {tilde over (M)}_(F).

The QR factorization may be performed by various methods, including aGram-Schmidt procedure, a householder transformation, and so on. TheGram-Schmidt procedure is recursive and may be numerically unstable.Various variants of the Gram-Schmidt procedure have been devised and areknown in the art. The “classical” Gram-Schmidt procedure fororthogonalizing the matrix {circumflex over (M)}^(T) is described below.

For QR factorization, the matrix {circumflex over (M)}^(T) may beexpressed as:{circumflex over (M)}^(T)=Q_(F)R_(F),  Eq(10)where

-   -   Q_(F) is an (N_(R)×N_(R)) orthogonal matrix; and    -   R_(F) is an (N_(R)×N_(T)) upper triangle matrix with zeros below        the diagonal and possible non-zero values along and above the        diagonal.

The Gram-Schmidt procedure generates the matrices Q_(F) and R_(F)column-by-column. The following notations are used for the descriptionbelow:

-   -   Q_(F)=[q₁ q₂ . . . q_(N) _(R) ], where q_(j) is the j-th column        of Q_(F);    -   q_(i,j) is the entry in the i-th row and j-th column of Q_(F);    -   {tilde over (Q)}_(F)=[{tilde over (q)}₁ {tilde over (q)}₂ . . .        {tilde over (q)}_(N) _(R) ], where {tilde over (q)}_(j) is the        j-th column of {tilde over (Q)}_(F);    -   r_(i,j) is the entry in the i-th row and j-th column of R_(F);    -   {circumflex over (M)}^(T)=[{circumflex over (m)}₁ {circumflex        over (m)}₂ . . . {circumflex over (m)}_(N) _(T) ], where        {circumflex over (m)}_(j) is the j-th column of {circumflex over        (M)}^(T); and    -   {circumflex over (m)}_(i,j) is the entry in the i-th row and        j-th column of {circumflex over (M)}^(T).

The first column of Q_(F) and R_(F) may be obtained as:

$\begin{matrix}{{r_{1,1} = {{{\underset{\_}{\hat{m}}}_{1}} = \left\lbrack {\sum\limits_{i = 1}^{N_{R}}\;{{\hat{m}}_{i,1}}^{2}} \right\rbrack^{1/2}}},{and}} & {{Eq}\mspace{20mu}(11)} \\{{\underset{\_}{q}}_{1} = {\frac{1}{r_{1,1}}{{\underset{\_}{\hat{m}}}_{1}.}}} & {{Eq}\mspace{20mu}(12)}\end{matrix}$The first column of R_(F) includes one non-zero value r_(1,1) for thefirst row and zeros elsewhere, where r_(1,1) is the 2-norm of{circumflex over (m)}₁. The first column of Q_(F) is a normalizedversion of the first column of {circumflex over (M)}^(T), where thenormalization is achieved by scaling each entry of {circumflex over(m)}₁ with the inverse of r_(1,1).

Each of the remaining columns of Q_(F) and R_(F) may be obtained asfollows:

$\begin{matrix}{{{{{FOR}\mspace{14mu} j} = 2},{3\mspace{14mu}\ldots\mspace{14mu} N_{T}}}{{{{FOR}\mspace{14mu} i} = 1},{{2\mspace{14mu}\ldots\mspace{14mu} j} - 1}}{r_{i,j} = {{\underset{\_}{q}}_{i}^{H}{\underset{\_}{\hat{m}}}_{j}}}} & {{Eq}\mspace{20mu}(13)} \\{{\underset{\_}{\overset{\sim}{q}}}_{j} = {{\underset{\_}{\hat{m}}}_{j} - {\sum\limits_{i = 1}^{j - 1}\;{r_{i,j} \cdot {\underset{\_}{q}}_{i}}}}} & {{Eq}\mspace{20mu}(14)} \\{r_{j,j} = {{\underset{\_}{\overset{\sim}{q}}}_{j}}} & {{Eq}\mspace{20mu}(15)} \\{{\underset{\_}{q}}_{j} = {\frac{1}{r_{j,j}}{{\underset{\_}{\overset{\sim}{q}}}_{j}.}}} & {{Eq}\mspace{20mu}(16)}\end{matrix}$

The Gram-Schmidt procedure generates one column at a time for the matrixQ_(F). Each new column of Q_(F) is forced to be orthogonal to allprior-generated columns to the left of the new column. This is achievedby equations (14) and (16), where the j-th column of Q_(F) (or q_(j)) isgenerated based on {tilde over (q)}_(j), which in turn is generatedbased on the j-th column of {circumflex over (M)}^(T) (or {circumflexover (m)}_(j)) and subtracting out any components in {circumflex over(m)}_(j) pointing in the direction of the other (j−1) columns to theleft of {circumflex over (m)}_(j). The diagonal elements of R_(F) arecomputed as the 2-norm of the columns of {tilde over (Q)}_(F) (where{tilde over (q)}₁={circumflex over (m)}₁), as shown in equation (15).

Improved performance may be attained by ordering the matrix {circumflexover (M)}^(T) based on the singular value estimates before performingthe QR factorization. The initial singular value estimates {tilde over(σ)}_(m), for m∈{1 . . . N_(T)}, for diagonal matrix {tilde over (Σ)}may be computed as the 2-norm of the columns of {circumflex over(M)}^(T), as described below. The initial singular value estimates maythen be ordered such that {{tilde over (σ)}₁≧{tilde over (σ)}₂≧ . . .≧{tilde over (σ)}_(N) _(T) }, where {tilde over (σ)}₁ is the largestsingular value estimate and {tilde over (σ)}_(N) _(T) is the smallestsingular value estimate. When the initial singular value estimates forthe diagonal matrix {tilde over (Σ)} are ordered, the columns of thematrix {circumflex over (M)}^(T) are also ordered correspondingly. Thefirst or left-most column of {circumflex over (M)}^(T) would then beassociated with the largest singular value estimate and the highestreceived SNR, and the last or right-most column of {circumflex over(M)}^(T) would be associated with the smallest singular value estimateand the lowest received SNR . For the QR factorization, the initialsingular value estimates may be obtained as the 2-norm of the columns of{circumflex over (M)}^(T) and used for ordering the columns of{circumflex over (M)}^(T). The final singular value estimates areobtained as the 2-norm of the columns of {tilde over (Q)}_(F), asdescribed above. The steered reference may also be transmitted in order(e.g., from the largest eigenmode to the smallest eigenmode), so thatthe singular value estimates are effectively ordered by the transmitter.

If the columns of {circumflex over (M)}^(T) are ordered based ondecreasing values of their associated singular value estimates, then thecolumns/eigenvectors of Q_(F) are forced to be orthogonal to the firstcolumn/eigenvector with the best received SNR. This ordering thus hasthe beneficial effect of rejecting certain noise components of each ofthe remaining eigenvectors of Q_(F). In particular, the j-th column ofQ_(F) (or q_(j)) is generated based on the j-th column of {circumflexover (M)}^(T) (or {circumflex over (m)}_(j)), and noise components in{circumflex over (m)}_(j) that point in the direction of the j−1eigenvectors to the left of q_(j) (which are associated with higherreceived SNRs) are subtracted from {circumflex over (m)}_(j) to obtainq_(j). The ordering also has the beneficial effect of improving theestimates of eigenvectors associated with smaller singular values. Theoverall result is improved performance, especially if the orthogonalizedeigenvectors of Q_(F) are used for spatial processing for datatransmission on the other link, as described below.

The enhanced orthogonal matched filter {tilde over (M)}_(F) obtainedbased on QR factorization may then be expressed as:{tilde over (M)}_(F) ^(T)=Q_(F){tilde over (R)}_(F),  Eq(17)where {tilde over (R)}_(F) includes only the diagonal elements of R_(F)(i.e., the elements above the diagonal are set to zeros). The diagonalelements of {tilde over (R)}_(F) and R_(F) are estimates of the singularvalues of H. Since M=Σ^(T)U^(H) and {tilde over (M)}_(F)={tilde over(R)}_(F) ^(T)Q_(F) ^(T), the following substitutions may be made: {tildeover (R)}_(F)≈Σ and Q_(F)≈U*, where “*” denotes the complex conjugate.2. Mean Square Error Computation and Polar Decomposition

The initial matched filter matrix {circumflex over (M)} may also beorthogonalized based on a particular optimality criterion. One possiblecriterion is to minimize a measure of the squared error between thematrix {circumflex over (M)} and an “optimum” matched filter with thedesired orthogonality properties. This may be expressed as:minimize ∥{circumflex over (M)}−Σ ^(T) Q _(P)∥_(F) subject to Q _(P)^(H) Q _(P) =I,  Eq(18)where ∥X∥_(F) is the Frobenius norm of X, and is given as:

$\begin{matrix}{{\underset{\_}{X}}_{F} = \left\lbrack {\sum\limits_{i,j}\;{x_{ij}}^{2}} \right\rbrack^{1/2}} & {{Eq}\mspace{20mu}(19)}\end{matrix}$The condition Q_(P) ^(H)Q_(P)=I ensures that Q_(P) is a unitary matrix,which would mean that the columns of Q_(P) are orthogonal to one anotherand the rows of Q_(P) are also orthogonal to one another. Equation (18)results in an optimum matched filter Σ^(T)Q_(P) that is the best fit tothe measured data given by the matrix {circumflex over (M)}.

The solution to equation (18) can be obtained from the known solution tothe orthogonal Procrustes problem. This problem asks the question—giventwo known matrices A and B, can a unitary matrix Q_(P) be found thatrotates B into A. The problem may be expressed as:minimize ∥A−BQ _(P)∥_(F) subject to Q _(P) ^(H) Q _(P) =I.  Eq(20)

The solution to the Procrustes problem can be obtained as follows.First, a matrix C_(P) is defined as C_(P)=B^(H)A. The singular valuedecomposition of C_(P) is then given as C_(P)=U_(P)Σ_(P)V_(P) ^(H) orU_(P) ^(H)C_(P)V_(P)=Σ_(P). The unitary matrix Q_(P) that solves theminimization problem shown in equation (20) is then given as:Q_(P)=U_(P)V_(P) ^(H).  Eq(21)The derivation and proof for equation (21) is described by G. H. Goluband C. F. Van Loan in “Matrix Computation”, Third Edition, Johns HopkinsUniversity Press, 1996.

The solution for equation (20), which is shown in equation (21), isrelated to the polar decomposition of the matrix C. This polardecomposition is given as:C_(P)=Z_(P)P_(P),  Eq(22)where

-   -   Z_(P) is a unitary matrix, which is given as Z_(P)=Ũ_(P)V_(P)        ^(H);    -   Ũ_(P) is a matrix of left eigenvectors of C_(P) that spans the        column space of C_(P) (i.e., Ũ_(P) is equal to U_(P) or a        sub-matrix of U_(P) depending on the dimension of C_(P));    -   P_(P) is a Hermitian symmetric positive semi-definite matrix,        which is given as P_(P)=V_(P){tilde over (Σ)}_(P)V_(P) ^(H); and    -   {tilde over (Σ)}_(P) is a square matrix of singular values of        C_(P) with dimension equal to the number of columns of C_(P).

Polar decomposition can thus be performed on the matrix C_(P) to obtainthe unitary matrix Z_(P), which may be equal to either Q_(P) or asub-matrix of Q_(P) depending on the dimension of C_(P). It can be shownthat the matrix Z_(P) is the optimal result to the minimization problemshown in equation (20).

Algorithms for direct computation of polar decomposition are describedby P. Zielinski and K. Zietak in “The Polar Decomposition—Properties,Applications and Algorithms,” Annals of the Polish Mathematical Society,38 (1995), and by A. A. Dubrulle in “An Optimum Iteration for the MatrixPolar Decomposition,” Electronic Transactions on Numerical Analysis,Vol. 8, 1999, pp. 21-25.

The solution for the optimum matched filter expressed in equation (18)may be obtained based on the solution to the orthogonal Procrustesproblem described above. This may be achieved by equating {circumflexover (M)} to A and Σ^(T) to B. For the computation, an estimate of thesingular values, {tilde over (Σ)}, may be obtained as the 2-norm of thecolumns of {circumflex over (M)}^(T) and used in place of Σ. Thediagonal elements of {tilde over (Σ)} may be expressed as:

$\begin{matrix}{{{\overset{\sim}{\sigma}}_{i,i} = {{{\hat{\underset{\_}{m}}}_{i}} = \left\lbrack {\sum\limits_{j = 1}^{\; N_{R}}\;{{\hat{m}}_{i,j}}^{2}} \right\rbrack^{1/2}}},{{{for}\mspace{14mu} i} \in {\left\{ {1\mspace{14mu}\ldots\mspace{14mu} N_{T}} \right\}.}}} & {{Eq}\mspace{20mu}(23)}\end{matrix}$It can be shown that the use of {tilde over (Σ)} in the computation forQ_(P) results in nearly un-measurable degradation in performancerelative to the use of the exact singular values in Σ.

A matrix C_(M) may then be defined as:C_(M)={tilde over (Σ)}{circumflex over (M)}.  Eq(24)The singular value decomposition of the matrix C_(M) is then given as:C_(M)=U_(M)Σ_(M)V_(M) ^(H) or U_(M) ^(H)C_(M)V_(M)=Σ_(M).  Eq(25)The unitary matrix Q_(M) that solves the minimization problem shown inequation (18) is then given as:Q_(M)=U_(M)V_(M) ^(H)≡Ũ^(H).  Eq(26)An enhanced orthogonal matched filter {tilde over (M)}_(M), which is thesolution to the minimization problem in equation (18), may then beexpressed as:{tilde over (M)}_(M)={tilde over (Σ)}^(T)Ũ^(H)={tilde over(Σ)}^(T)U_(M)V_(M) ^(H).  Eq(27)

Alternatively, the polar decomposition of C_(M) may be performed asdescribed above, which may be expressed as:C_(M)=Z_(M)P_(M).  Eq(28)The unitary matrix Q_(M) that solves the minimization problem shown inequation (18) may then be given as:Q_(M)=Z_(M)≡Ũ^(H).  Eq(29)

The enhanced orthogonal matched filter {tilde over (M)}_(M) may then beexpressed as:{tilde over (M)}_(M)={tilde over (Σ)}^(T)Z_(M).  Eq(30)It can be shown that the matrix Z_(M) from the polar decomposition isthe optimal result for the matrix Q_(M) for the minimum square errorcomputation (i.e., Q_(M)=Z_(M)). Thus, the polar decomposition andminimum square error computation both yield the same orthogonal matchedfilter {tilde over (M)}_(M).

FIG. 1 shows a flow diagram of an embodiment of a process 100 forderiving an orthogonal matched filter matrix {tilde over (M)} based on asteered reference. Initially, the receiver receives and processes thesteered reference to obtain an estimate of u_(m)σ_(m) or for each ofmultiple eigenmodes of H (step 112). This processing may be performed asdescribed above. An initial matched filter matrix {circumflex over (M)}is then formed whose rows {circumflex over (m)}_(m), for m∈{1 . . .N_(T)}, are derived based on the estimates of u_(m)σ_(m). The orthogonalmatched filter matrix {tilde over (M)} may then be obtained from theinitial matched filter matrix {circumflex over (M)} using any one of theorthogonalization techniques described above.

For the QR factorization technique, the matrix {circumflex over (M)} isfactorized to obtain the matrices Q_(F) and R_(F) (step 122). Theorthogonal matched filter matrix {tilde over (M)} is then obtained asshown in equation (17) (step 124) and the singular value estimates{tilde over (Σ)} are obtained as the diagonal elements of R_(F) (step126).

For the minimum square error technique, estimates of the singularvalues, {tilde over (Σ)}, are obtained as the 2-norm of the columns of{circumflex over (M)}^(T) (step 132). The matrix C_(M) is then computedas shown in equation (24) (step 134). Singular value decomposition ofC_(M) is next computed as shown in equation (25) (step 136). Theorthogonal matched filter matrix {tilde over (M)} is then obtained asshown in equation (27) (step 138).

For the polar decomposition technique, estimates of the singular values,{tilde over (Σ)}, are obtained as the 2-norm of the columns of{circumflex over (M)}^(T) (step 142). The matrix C_(M) is then computedas shown in equation (24) (step 144). Polar decomposition of C_(M) isnext computed as shown in equation (28) (step 146). The orthogonalmatched filter matrix {tilde over (M)} is then obtained as shown inequation (30) (step 148).

The orthogonal matched filter matrix {tilde over (M)} may thereafter beused to perform matched filtering of a received data transmission (step150).

The orthogonalization of the matched filter matrix provides severalbenefits. First, the use of an orthogonal matched filter matrix {tildeover (M)} avoids cross-talk between the eigenmodes of H. The derivationof the initial matched filter matrix {circumflex over (M)} piecemealbased on the steered reference does not guarantee that the eigenvectorsof {circumflex over (M)}^(T) are orthogonal. The lack of orthogonalityresults in performance degradation. The orthogonalization of the matchedfilter matrix avoids this performance degradation.

Second, QR factorization can improve the quality of the eigenvectorsassociated with smaller singular values. Without QR factorization, thequality of the estimates of the eigenvectors is not constant, and theestimates of the eigenvectors associated with smaller singular valuesare likely to be lower in quality. QR factorization can improve thequality of the eigenvectors associated with smaller singular values byrejecting certain noise components, as described above. Polardecomposition may have similar effect, but not in the direct way as QRfactorization.

Third, orthogonalization may reduce the amount of resources needed totransmit the steered reference. If orthogonalization is not performed,then high quality estimates of Σ and U would be needed to ensure lowcross-talk among the eigenmodes. A longer transmission period would thenbe needed for the steered reference for the eigenvectors associated withsmaller singular values to ensure that the desired quality is obtained.High quality estimates of Σ and U would thus require a longer period oftransmission for the steered reference (which would consume morevaluable system resources) and a longer integration period for thesteered reference at the receiver (which may result in longer delay fordata transmission). Orthogonalization can provide the desiredperformance without the need for high quality estimates of Σ and U.

III. MIMO-OFDM System

The techniques for deriving eigenvectors used for spatial processing arenow described for an exemplary wideband MIMO communication system thatemploys orthogonal frequency division multiplexing (OFDM). OFDMeffectively partitions the overall system bandwidth into a number of(N_(F)) orthogonal subbands, which are also referred to as tones,frequency bins, or frequency subchannels. With OFDM, each subband isassociated with a respective subcarrier upon which data may bemodulated. For a MIMO-OFDM system, each subband may be associated withmultiple eigenmodes, and each eigenmode of each subband may be viewed asan independent transmission channel.

For OFDM, the data or pilot to be transmitted on each usable subband isfirst modulated (i.e., mapped to modulation symbols) using a particularmodulation scheme. One modulation symbol may be transmitted on eachusable subband in each symbol period. A signal value of zero may be sentfor each unused subband. For each OFDM symbol period, the modulationsymbols for the usable subbands and zero signal values for the unusedsubbands (i.e., the modulation symbols and zeros for all Nsubbands) aretransformed to the time domain using an inverse fast Fourier transform(IFFT) to obtain a transformed symbol that comprises N_(F) time-domainsamples. To combat inter-symbol interference (ISI) caused by frequencyselective fading, a portion of each transformed symbol is often repeated(which is often referred to as adding a cyclic prefix) to form acorresponding OFDM symbol. The OFDM symbol is then processed andtransmitted over the wireless channel. An OFDM symbol period, which isalso referred to as a symbol period, corresponds to the duration of oneOFDM symbol.

For this exemplary system, the downlink and uplink share a singlefrequency band using time-division duplex (TDD). For a TDD MIMO-OFDMsystem, the downlink and uplink channel responses may be assumed to bereciprocal of one another. That is, if H(k) represents a channelresponse matrix from antenna array A to antenna array B for subband k,then a reciprocal channel implies that the coupling from array B toarray A is given by H^(T)(k).

FIG. 2 shows a wireless communication system 200 that includes a numberof access points (APs) 210 that communicate with a number of userterminals (UTs) 220. (For simplicity, only one access point is shown inFIG. 2.) An access point may also be referred to as a base station orsome other terminology. Each user terminal may be a fixed or mobileterminal and may also be referred to as an access terminal, a mobilestation, a remote station, a user equipment (UE), a wireless device, orsome other terminology. Each user terminal may communicate with one orpossibly multiple access points on the downlink and/or the uplink at anygiven moment. The downlink (i.e., forward link) refers to transmissionfrom the access point to the user terminal, and the uplink (i.e.,reverse link) refers to transmission from the user terminal to theaccess point. The channel response between each access point and eachuser terminal may be characterized by a set of channel response matricesH(k), for k∈K where K represents the set of all subbands of interest(e.g., the usable subbands).

In the following description for a pair of communicating access pointand user terminal, it is assumed that calibration has been performed toaccount for differences between the transmit and receive chains of theaccess point and the user terminal. The results of the calibration arediagonal matrices {circumflex over (K)}_(ap)(k) and {circumflex over(K)}_(ut)(k), for k∈K, to be used at the access point and the userterminal, respectively, on the transmit path. A “calibrated” downlinkchannel response, H_(cdn)(k), observed by the user terminal and a“calibrated” uplink channel response, H_(cup)(k), observed by the accesspoint may then be expressed as:H _(cdn)(k)=H _(dn)(k){circumflex over (K)} _(ap)(k), for k∈K,  Eq(31a)H _(cup)(k)=H _(up)(k){circumflex over (K)} _(ut)(k), for k∈K,and  Eq(31b)H _(cdn)(k)≈H _(cup) ^(T)(k), for k∈K,  Eq(31c)where

-   -   H_(dn)(k)=R_(ut)(k)H(k)T_(ap)(k) is the “effective” downlink        channel response, which includes the responses of the transmit        chain T_(ap)(k) at the access point and the receive chain        R_(ut)(k) at the user terminal;    -   H_(up)(k)=R_(ap)(k)H^(T)(k)T_(ut)(k) is the “effective” uplink        channel response, which includes the responses of the transmit        chain T_(ut)(k) at the user terminal and the receive chain        R_(ap)(k) at the access point; and    -   H(k) is an (N_(ut)×N_(ap)) channel response matrix between the        N_(ap) antennas at the access point and the N_(ut) antennas at        the user terminal.        If calibration is not performed, then the matrices {circumflex        over (K)}_(ap)(k) and {circumflex over (K)}_(ut)(k), for k∈K,        are each set to the identity matrix I.

FIG. 3 shows an embodiment of a frame structure 300 that may be used fora TDD MIMO-OFDM system. Data transmission occurs in units of TDD frames,with each TDD frame covering a particular time duration (e.g., 2 msec).Each TDD frame is partitioned into a downlink phase and an uplink phase.The downlink phase is further partitioned into multiple segments formultiple downlink transport channels. In the embodiment shown in FIG. 3,the downlink transport channels include a broadcast channel (BCH), aforward control channel (FCCH), and a forward channel (FCH). Similarly,the uplink phase is partitioned into multiple segments for multipleuplink transport channels. In the embodiment shown in FIG. 3, the uplinktransport channels include a reverse channel (RCH) and a random accesschannel (RACH).

In the downlink phase, a BCH segment 310 is used to transmit one BCHprotocol data unit (PDU) 312, which includes a beacon pilot 314, a MIMOpilot 316, and a BCH message 318. The beacon pilot is transmitted fromall access point antennas and is used by the user terminals for timingand frequency acquisition. The MIMO pilot is transmitted from all accesspoint antennas with different orthogonal codes and is used by the userterminals for channel estimation. The BCH message carries systemparameters for the user terminals in the system. An FCCH segment 320 isused to transmit one FCCH PDU, which carries assignments for downlinkand uplink resources and other signaling for the user terminals. An FCHsegment 330 is used to transmit one or more FCH PDUs 332. Differenttypes of FCH PDU may be defined. For example, an FCH PDU 332 a includesonly a data packet 336 a, and an FCH PDU 332 b includes a downlinksteered reference 334 b and a data packet 336 b.

In the uplink phase, an RCH segment 340 is used to transmit one or moreRCH PDUs 342 on the uplink. Different types of RCH PDU may also bedefined. For example, an RCH PDU 342 a includes an uplink steeredreference 344 a and a data packet 346 a. An RACH segment 350 is used bythe user terminals to gain access to the system and to send shortmessages on the uplink. An RACH PDU 352 may be sent within RACH segment350 and includes an uplink steered reference 354 and a message 356.

For the embodiment shown in FIG. 3, the beacon and MIMO pilots are senton the downlink in the BCH segment in each TDD frame. A steeredreference may or may not be sent in any given FCH/RCH PDU. A steeredreference may also be sent in an RACH PDU to allow the access point toestimate pertinent vectors during system access.

For simplicity, the following description is for a communication betweenone access point and one user terminal. The MIMO pilot is transmitted bythe access point and used by the user terminal to obtain an estimate ofthe calibrated downlink channel response, Ĥ_(cdn)(k), for k∈K. Thecalibrated uplink channel response may then be estimated asĤ_(cup)(k)=Ĥ_(cdn) ^(T)(k). Singular value decomposition may beperformed to diagonalized the matrix Ĥ_(cup)(k) for each subband, whichmay be expressed as:Ĥ _(cup)(k)=Û _(ap)(k){circumflex over (Σ)}(k){circumflex over (V)}_(ut) ^(H)(k), for k∈K,  Eq(32)where

-   -   Û_(ap)(k) is an (N_(ap)×N_(ap)) unitary matrix of left        eigenvectors of Ĥ_(cup)(k);    -   {circumflex over (Σ)}(k) is an (N_(ap)×N_(ut)) diagonal matrix        of singular values of Ĥ_(cup)(k); and    -   {circumflex over (V)}_(ut)(k) is an (N_(ut)×N_(ut)) unitary        matrix of right eigenvectors of Ĥ_(cup)(k).

Similarly, the singular value decomposition of the estimated calibrateddownlink channel response matrix, Ĥ_(cdn)(k), may be expressed as:Ĥ _(cdn)(k)={circumflex over (V)} _(ut)*(k){circumflex over (Σ)}(k)Û_(ap) ^(T)(k), for k∈K,  Eq(33)where the matrices {circumflex over (V)}_(ut)*(k) and Û_(ap)*(k) areunitary matrices of left and right eigenvectors, respectively, ofĤ_(cdn)(k).

As shown in equations (32) and (33), the matrices of left and righteigenvectors for one link are the complex conjugate of the matrices ofright and left eigenvectors, respectively, for the other link. Forsimplicity, reference to the matrices Û_(ap)(k) and {circumflex over(V)}_(ut)(k) in the following description may also refer to theirvarious other forms (e.g., {circumflex over (V)}_(ut)(k) may refer to{circumflex over (V)}_(ut)(k), {circumflex over (V)}*_(ut)(k),{circumflex over (V)}_(ut) ^(T)(k), and {circumflex over (V)}_(ut)^(H)(k)). The matrices Û_(ap)(k) and {circumflex over (V)}_(ut)(k) maybe used by the access point and user terminal, respectively, for spatialprocessing and are denoted as such by their subscripts. The matrix{circumflex over (Σ)}(k) includes singular value estimates thatrepresent the gains for the independent channels (or eigenmodes) of thechannel response matrix H(k) for the k-th subband.

The singular value decomposition may be performed independently for thechannel response matrix Ĥ_(cup)(k) for each of the usable subbands todetermine the N_(S) eigenmodes for the subband. The singular valueestimates for each diagonal matrix {circumflex over (Σ)}(k) may beordered such that {{circumflex over (σ)}₁(k)≧{circumflex over (σ)}₂(k)≧. . . ≧{circumflex over (σ)}_(N) _(S) (k)}, where {circumflex over(σ)}₁(k) is the largest singular value estimate and {circumflex over(σ)}_(N) _(S) (k) is the smallest singular value estimate for subband k.When the singular value estimates for each diagonal matrix {circumflexover (Σ)}(k) are ordered, the eigenvectors (or columns) of theassociated matrices Û(k) and {circumflex over (V)}(k) are also orderedcorrespondingly. After the ordering, {circumflex over (σ)}₁(k)represents the singular value estimate for the best eigenmode forsubband k, which is also often referred to as the “principal” eigenmode.

A “wideband” eigenmode may be defined as the set of same-ordereigenmodes of all subbands after the ordering. Thus, the m-th widebandeigenmode includes the m-th eigenmodes of all subbands. Each widebandeigenmode is associated with a respective set of eigenvectors for all ofthe subbands. The “principal” wideband eigenmode is the one associatedwith the largest singular value estimate in the matrix {circumflex over(Σ)}(k) for each of the subbands.

The user terminal can transmit a steered reference on the uplink. Theuplink steered reference for the m-th wideband eigenmode may beexpressed as:x _(up,sr,m)(k)={circumflex over (K)} _(ut)(k){circumflex over (v)}_(ut,m)(k)p(k), for k∈K,   Eq(34)where

-   -   {circumflex over (v)}_(ut,m)(k) is the m-th column of the matrix        {circumflex over (V)}_(ut)(k) for the k-th subband, with        {circumflex over (V)}_(ut)(k)=[{circumflex over        (v)}_(ut,1)(k){circumflex over (v)}_(ut,2)(k) . . . {circumflex        over (v)}_(ut,N) _(ut) (k)]; and    -   p(k) is the pilot symbol for the k-th subband.

The received uplink steered reference at the access point may beexpressed as:

$\begin{matrix}\begin{matrix}{\underset{\_}{r}}_{{up},{sr},m} & {= {{{{\underset{\_}{H}}_{up}(k)}{{\underset{\_}{x}}_{{up},{sr},m}(k)}} + {{\underset{\_}{n}}_{up}(k)}}} & {,{{{for}\mspace{14mu} k} \in K},} \\\; & {= {{{{\underset{\_}{H}}_{up}(k)}{{\underset{\_}{\hat{K}}}_{ut}(k)}{{\underset{\_}{\hat{v}}}_{{ut},m}(k)}{p(k)}} + {{\underset{\_}{n}}_{up}(k)}}} & \; \\\; & {\approx {{{{\underset{\_}{\hat{u}}}_{{ap},m}(k)}{{\hat{\sigma}}_{m}(k)}{p(k)}} + {{\underset{\_}{n}}_{up}(k)}}} & \;\end{matrix} & {{Eq}\mspace{20mu}(35)}\end{matrix}$where

-   -   û_(ap,m)(k) is the m-th column of the matrix Û_(ap)(k) for the        k-th subband, with Û_(ap)(k)=[û_(ap,1)(k)û_(ap,2)(k) . . .        û_(ap,N) _(ap) (k)]; and    -   {circumflex over (σ)}_(m)(k) is the singular value estimate for        the k-th subband of the m-th wideband eigenmode.

The access point can obtain an initial matched filter matrix {circumflexover (M)}_(ap)(k), for k∈K, based on the uplink steered reference, asdescribed above. The access point may thereafter obtain an enhancedorthogonal matched filter matrix {tilde over (M)}_(ap)(k), for k∈K,based on {circumflex over (M)}_(ap)(k) and using any one of theorthogonalization techniques described above.

Using QR factorization, the matrix {tilde over (M)}_(ap)(k) may beobtained as:{tilde over (M)} _(ap) ^(T)(k)=Q _(ap)(k){tilde over (R)} _(ap)(k),or  Eq(36a){tilde over (M)} _(ap)(k)={tilde over (R)} _(ap) ^(T)(k)Q _(ap)^(T)(k)={tilde over (Σ)}_(ap) ^(T)(k)Ũ _(ap) ^(H)(k),  Eq(36b)where

-   -   Q_(ap)(k) is a unitary matrix that is the ortho-normal basis for        {tilde over (M)}_(ap)(k);    -   {tilde over (R)}_(ap)(k) is a diagonal matrix derived based on        {circumflex over (M)}_(ap)(k); and    -   {tilde over (Σ)}_(ap)(k)={tilde over (R)}_(ap)(k) and        Ũ_(ap)*(k)=Q_(ap)(k).

Using mean square error computation, the matrix {tilde over (M)}_(ap)(k)may be obtained as:{tilde over (M)} _(ap)(k)={tilde over (Σ)}_(ap) ^(T)(k)U _(Map)(k)V_(Map) ^(H)(k)={tilde over (Σ)}_(ap) ^(T)(k)Ũ _(ap) ^(H)(k), fork∈K,  Eq(37)whereC _(ap)(k)={tilde over (Σ)}_(ap)(k){circumflex over (M)} _(ap)(k)=U_(Map)(k)Σ_(Map)(k)V _(Map) ^(H)(k); for k∈K,  Eq(38)

-   -   {tilde over (Σ)}_(ap)(k) is the diagonal matrix whose elements        are the 2-norm of the columns of {circumflex over (M)}_(ap)        ^(T)(k); and        Ũ _(ap) ^(H)(k)=U _(Map)(k)V _(Map) ^(H)(k).

Using polar decomposition, the matrix {tilde over (M)}_(ap)(k) may beobtained as:{tilde over (M)} _(ap)(k)={tilde over (Σ)}_(ap) ^(T)(k)Z _(ap)(k)={tildeover (Σ)}_(ap) ^(T)(k)Ũ _(ap) ^(H)(k), for k∈K.  Eq(39)whereC _(ap)(k)={tilde over (Σ)}_(ap)(k){circumflex over (M)} _(ap)(k)=Z_(ap)(k)P _(ap)(k), for k∈K; and  Eq(40)Ũ _(ap) ^(H)(k)=Z _(ap)(k).

The matrix {tilde over (M)}_(ap)(k) may be used by the access point formatched filtering of uplink data transmission from the user terminal, asdescribed below.

The spatial processing performed by the user terminal to transmit dataon multiple eigenmodes on the uplink may be expressed as:x _(up)(k)={circumflex over (K)} _(ut)(k){circumflex over (V)} _(ut)(k)s_(up)(k), for k∈K,  Eq(41)where s_(up)(k) is the data vector and x_(up)(k) is the transmit vectorfor the k-th subband for the uplink. Uplink data transmission can occuron any number of wideband eigenmodes from 1 to N_(S).

The received uplink data transmission at the access point may beexpressed as:

$\begin{matrix}\begin{matrix}{{{\underset{\_}{r}}_{up}(k)} = {{{{\underset{\_}{H}}_{up}(k)}{{\underset{\_}{x}}_{up}(k)}} + {{\underset{\_}{n}}_{up}(k)}}} \\{{= {{{{\underset{\_}{H}}_{up}(k)}{{\underset{\_}{\hat{K}}}_{ut}(k)}{{\underset{\_}{\hat{V}}}_{ut}(k)}{{\underset{\_}{s}}_{up}(k)}} + {{\underset{\_}{n}}_{up}(k)}}},} \\{{{{for}\mspace{14mu} k} \in K},} \\{= {{{{\underset{\_}{\hat{U}}}_{ap}(k)}{\underset{\_}{\hat{\Sigma}}(k)}{{\underset{\_}{s}}_{up}(k)}} + {{\underset{\_}{n}}_{up}(k)}}}\end{matrix} & {{Eq}\mspace{20mu}(42)}\end{matrix}$where r_(up)(k) is the receive vector for the uplink data transmissionfor the k-th subband.

The matched filtering by the access point may be expressed as:

$\begin{matrix}\begin{matrix}{{{\underset{\_}{\hat{s}}}_{up}(k)} = {{{\underset{\_}{G}}_{ap}(k)}{{\underset{\_}{\overset{\sim}{M}}}_{ap}(k)}{{\underset{\_}{r}}_{up}(k)}}} \\{{= {{{\underset{\_}{G}}_{ap}(k)}{{\overset{\sim}{\underset{\_}{\Sigma}}}_{ap}^{T}(k)}\;{{\underset{\_}{\overset{\sim}{U}}}_{ap}^{H}\left( {{{{\hat{\underset{\_}{U}}}_{ap}(k)}{\underset{\_}{\hat{\Sigma}}(k)}{{\underset{\_}{s}}_{up}(k)}} + {{\underset{\_}{n}}_{up}(k)}} \right)}}},} \\{{{{for}\mspace{14mu} k} \in K},} \\{\approx {{{\underset{\_}{s}}_{up}(k)} + {{\underset{\_}{\overset{\sim}{n}}}_{up}(k)}}}\end{matrix} & {{Eq}\mspace{20mu}(43)}\end{matrix}$where

-   -   {tilde over (Σ)}(k)=diag ({tilde over (σ)}_(1,1)(k) {tilde over        (σ)}_(2,2)(k) . . . {tilde over (σ)}_(N) _(T) _(,N) _(T) (k));        and    -   G_(ap)(k)=diag(1/{tilde over (σ)}_(1,1) ²) (k) 1/{tilde over        (σ)}_(2,2) ²(k) . . . 1/{tilde over (σ)}_(N) _(T) _(,N) _(T)        ²(k)).

For the TDD MIMO system, the access point may also use the matricesŨ_(ap)(k), for k∈K, for spatial processing for data transmission on thedownlink to the user terminal. The spatial processing performed by theaccess point to transmit data on multiple eigenmodes on the downlink maybe expressed as:x _(dn)(k)={circumflex over (K)} _(ap)(k)Û_(ap)* (k)s _(dn)(k), fork∈K,  Eq(44)where s_(dn)(k) is the data vector and x_(dn)(k) is the transmit vectorfor the k-th subband for the downlink. Downlink data transmission cansimilarly occur on any number of wideband eigenmodes from 1 to N_(S).

The received downlink data transmission at the user terminal may beexpressed as:

$\begin{matrix}\begin{matrix}{{{\underset{\_}{r}}_{dn}(k)} = {{{{\underset{\_}{H}}_{dn}(k)}{{\underset{\_}{x}}_{dn}(k)}} + {{\underset{\_}{n}}_{dn}(k)}}} \\{{= {{{{\underset{\_}{H}}_{dn}(k)}{{\underset{\_}{\hat{K}}}_{ap}(k)}{{\underset{\_}{\overset{\sim}{U}}}_{ap}^{*}(k)}{{\underset{\_}{s}}_{dn}(k)}} + {{\underset{\_}{n}}_{dn}(k)}}},} \\{{{{for}\mspace{14mu} k} \in K},} \\{= {{{{\underset{\_}{\hat{V}}}_{ut}^{*}(k)}{\underset{\_}{\hat{\Sigma}}(k)}{{\underset{\_}{s}}_{dn}(k)}} + {{\underset{\_}{n}}_{dn}(k)}}}\end{matrix} & {{Eq}\mspace{20mu}(45)}\end{matrix}$where r_(dn)(k) is the receive vector for the downlink data transmissionfor the k-th subband.

The matched filtering by the user terminal may be expressed as:

$\begin{matrix}\begin{matrix}{{{\underset{\_}{\hat{s}}}_{dn}(k)} = {{{\underset{\_}{G}}_{ut}(k)}{{\underset{\_}{\hat{M}}}_{ut}(k)}{{\underset{\_}{r}}_{dn}(k)}}} \\{{= {{{\underset{\_}{G}}_{ut}(k)}{{\underset{\_}{\hat{\Sigma}}}^{T}(k)}\;{{\underset{\_}{\hat{V}}}_{ut}^{T}(k)}\left( {{{{\underset{\_}{\hat{V}}}_{ut}^{*}(k)}{\underset{\_}{\hat{\Sigma}}(k)}{{\underset{\_}{s}}_{dn}(k)}} + {{\underset{\_}{n}}_{dn}(k)}} \right)}},} \\{{{{for}\mspace{14mu} k} \in K},} \\{\approx {{{\underset{\_}{s}}_{dn}(k)} + {{\underset{\_}{\overset{\sim}{n}}}_{dn}(k)}}}\end{matrix} & {{Eq}\mspace{20mu}(46)}\end{matrix}$where

-   -   {circumflex over (M)}_(ut)(k)={circumflex over        (Σ)}^(T)(k){circumflex over (V)}_(ut) ^(T)(k) is the matched        filter for the user terminal;    -   {circumflex over (Σ)}(k)=diag ({circumflex over        (σ)}_(1,1)(k){circumflex over (σ)}_(2,2)(k) . . . {circumflex        over (σ)}_(N) _(S) _(,N) _(S) (k)); and    -   G_(ut)(k)=diag (1/{circumflex over (σ)}_(1,1) ²(k) 1/{circumflex        over (σ)}_(2,2) ²(k) . . . 1/{circumflex over (σ)}_(N) _(S)        _(,N) _(S) ²(k)).        The diagonal matrix {circumflex over (Σ)}(k) is derived from the        singular value decomposition shown in equation (32).

Table 1 summarizes the spatial processing at the access point and userterminal for both data transmission and reception on multiple widebandeigenmodes.

TABLE 1 Downlink Uplink Access Transmit: Receive: Point x _(dn) (k) = ŝ_(up) (k) = {circumflex over (K)} _(ap) (k)Ũ*_(ap) (k)s _(dn) (k) G_(ap) (k){tilde over (Σ)} ^(T) (k)Ũ ^(H) _(ap) (k)r _(up) (k) UserReceive: Transmit: Terminal ŝ _(dn) (k) = x_(up) (k) = G _(ut)(k){circumflex over (Σ)} ^(T) (k){circumflex over (V)} _(ut) ^(T) (k)r_(dn) (k) {circumflex over (K)} _(ut) (k){circumflex over (V)} _(ut)(k)s _(up) (k)In Table 1, s(k) is the data vector, x(k) is the transmit vector, r(k)is the receive vector, and ŝ(k) is an estimate of the data vector s(k),where all vectors are for subband k. The subscripts “dn” and “up” forthese vectors denote downlink and uplink transmissions, respectively.

It can be shown that the use of the matrices Ũ_(ap)(k), for k∈K, (withorthogonalized columns) for spatial processing for downlink datatransmission can provide substantial improvement over the use ofmatrices {circumflex over (Û)}_(ap)(k), for k∈K, (with un-orthogonalizedcolumns) obtained from the initial matched filter matrices {circumflexover (M)}_(ap)(k), for k∈K.

FIG. 4 shows transmission of steered reference and data on the downlinkand uplink for an exemplary transmission scheme. The MIMO pilot istransmitted on the downlink by the access point in each TDD frame (block412). The user terminal receives and processes the downlink MIMO pilotto obtain an estimate the downlink channel response Ĥ_(cdn)(k), for k∈K.The user terminal then estimates the uplink channel response asĤ_(cup)(k)=Ĥ_(cdn) ^(T)(k) and performs singular value decomposition ofĤ_(cup)(k) to obtain the matrices {circumflex over (Σ)}(k) and{circumflex over (V)}_(ut)(k), for k∈K, as shown in equation (32) (block414).

The user terminal then transmits the uplink steered reference on theRACH or the RCH using the matrices {circumflex over (V)}_(ut)(k), fork∈K, as shown in equation (34) and FIG. 3, during system access (step422). The columns of {circumflex over (V)}_(ut)(k) are also referred toas steering vectors when used for data transmission. The access pointreceives and processes the uplink steered reference on the RACH or theRCH to obtain the matrices {tilde over (Σ)}(k) and Ũ_(ap)(k), for k∈K,as described above (step 424). The columns of Ũ_(ap)(k) are eigenvectorsthat may be used for both data reception as well as data transmission.The user terminal may thereafter transmit the uplink steered referenceand data on the RCH using the matrices {circumflex over (V)}_(ut)(k),for k∈K, as shown in equation (41) and FIG. 3 (step 432). The accesspoint receives and processes the uplink steered reference on the RCH toupdate the matrices {tilde over (Σ)}(k) and Ũ_(ap)(k), for k∈K (step434). The access point also performs matched filtering for the receiveduplink data transmission using the matrices {tilde over (Σ)}(k) andŨ_(ap)(k) (also step 434).

The access point may thereafter transmit an optional downlink steeredreference and data on the FCH using the matrices Ũ_(ap)(k), for k∈K, asshown in equation (44) and FIG. 3 (step 442). If a downlink steeredreference is transmitted, then the user terminal can process thedownlink steered reference to update the matrices {circumflex over(Σ)}(k) and {circumflex over (V)}_(ut)(k), for k∈K (step 444) and mayalso perform orthogonalization to ensure that the columns of {circumflexover (V)}_(ut)(k) are orthogonal. The user terminal also performsmatched filtering for the received downlink data transmission using thematrices {circumflex over (Σ)}(k) and {circumflex over (V)}_(ut)(k)(also step 444).

The pilot and data transmission scheme shown in FIG. 4 provides severaladvantages. First, the MIMO pilot transmitted by the access point may beused by multiple user terminals in the system to estimate the responseof their respective MIMO channels. Second, the computation for thesingular value decomposition of Ĥ_(cup)(k), for k∈K, is distributedamong the user terminals (i.e., each user terminal performs singularvalue decomposition of its own set of estimated channel responsematrices for the usable subbands). Third, the access point can obtainthe matrices {tilde over (Σ)}(k) and Ũ_(ap)(k), for k∈K, which are usedfor uplink and downlink spatial processing, based on the steeredreference without having to estimate the MIMO channel response.

Various other transmission schemes may also be implemented for MIMO andMIMO-OFDM systems, and this is within the scope of the invention. Forexample, the MIMO pilot may be transmitted by the user terminal and thesteered reference may be transmitted by the access point.

FIG. 5 shows a block diagram of an embodiment of an access point 210 xand a user terminal 220 x in MIMO-OFDM system 200. For clarity, in thisembodiment, access point 210 x is equipped with four antennas that canbe used for data transmission and reception, and user terminal 220 x isalso equipped with four antennas for data transmission/reception. Ingeneral, the access point and user terminal may each be equipped withany number of transmit antennas and any number of receive antennas.

On the downlink, at access point 210 x, a transmit (TX) data processor514 receives traffic data from a data source 512 and signaling and otherdata from a controller 530. TX data processor 514 formats, codes,interleaves, and modulates the data to provide modulation symbols, whichare also referred to as data symbols. A TX spatial processor 520 thenreceives and multiplexes the data symbols with pilot symbols, performsthe required spatial processing with the matrices Ũ_(ap)*(k), for k∈K,and provides four streams of transmit symbols for the four transmitantennas. Each modulator (MOD) 522 receives and processes a respectivetransmit symbol stream to provide a corresponding downlink modulatedsignal. The four downlink modulated signals from modulators 522 athrough 522 d are then transmitted from antennas 524 a through 524 d,respectively.

At user terminal 220 x, four antennas 552 a through 552 d receive thetransmitted downlink modulated signals, and each antenna provides areceived signal to a respective demodulator (DEMOD) 554. Eachdemodulator 554 performs processing complementary to that performed bymodulator 522 and provides received symbols. A receive (RX) spatialprocessor 560 then performs matched filtering on the received symbolsfrom all demodulators 554 a through 554 d to provide recovered datasymbols, which are estimates of the data symbols transmitted by theaccess point. An RX data processor 570 further processes (e.g., symboldemaps, deinterleaves, and decodes) the recovered data symbols toprovide decoded data, which may be provided to a data sink 572 forstorage and/or a controller 580 for further processing.

RX spatial processor 560 also processes the received pilot symbols toobtain an estimate of the downlink channel response, Ĥ_(cdn)(k), fork∈K. Controller 580 may then decompose each matrix Ĥ_(cdn)(k) to obtain{circumflex over (Σ)}(k) and {circumflex over (V)}_(ut)(k). Controller580 may further derive (1) the downlink matched filter matrices{circumflex over (M)}_(ut)(k), for k∈K, based on {circumflex over(Σ)}(k) and {circumflex over (V)}_(ut)(k), and (2) the scaling matricesG_(ut)(k), for k∈K, based on {circumflex over (Σ)}(k). Controller 580may then provide {circumflex over (M)}_(ut)(k) to RX data processor 560for downlink matched filtering and {circumflex over (V)}_(ut)(k) to a TXspatial processor 590.

The processing for the uplink may be the same or different from theprocessing for the downlink. Data and signaling are processed (e.g.,coded, interleaved, and modulated) by a TX data processor 588,multiplexed with pilot symbols, and further spatially processed by TXspatial processor 590 with the matrices {circumflex over (V)}_(ut)(k),for k∈K. The transmit symbols from TX spatial processor 590 are furtherprocessed by modulators 554 a through 554 d to generate four uplinkmodulated signals, which are then transmitted via antennas 552 a through552 d.

At access point 510, the uplink modulated signals are received byantennas 524 a through 524 d and demodulated by demodulators 522 athrough 522 d to provide received symbols for the uplink steeredreference and data transmission. An RX spatial processor 540 thenprocesses the received uplink steered reference to obtain estimates ofu_(m)σ_(m), for k∈K and m∈{1 . . . N_(S)}, which are provided tocontroller 530. Controller then obtains {circumflex over (M)}_(ap)(k)and {tilde over (Σ)}(k) based on the estimates of u_(m)σ_(m), performsorthogonalization of {circumflex over (M)}_(ap)(k) to obtain {tilde over(M)}_(ap)(k) and Ũ_(ap)(k), and derives G_(ap)(k) based on {tilde over(Σ)}(k). Controller 580 then provides {tilde over (M)}_(ap)(k) andG_(ap)(k) to RX spatial processor 540 for uplink matched filtering andŨ_(ap)*(k) to TX spatial processor 520 for downlink spatial processing.

RX spatial processor 540 performs matched filtering of the receiveduplink data transmission with {tilde over (M)}_(ap)(k) and G_(ap)(k) toprovide recovered data symbols, which are further processed by an RXdata processor 542 to provide decoded data. The decoded data may beprovided to a data sink 544 for storage and/or controller 530 forfurther processing.

Controller 530 performs the processing to obtain the matched filtermatrices {tilde over (M)}_(ap)(k) and the scaling matrices G_(ap)(k),for k∈K, for uplink data transmission and the matrices Ũ_(ap)*(k), fork∈K, for downlink data transmission. Controller 580 performs theprocessing to obtain the matched filter matrices {circumflex over(M)}_(ut)(k) and the scaling matrices G_(ut)(k), for k∈K, for downlinkdata transmission and the matrices {circumflex over (V)}_(ut)(k), fork∈K, for uplink data transmission. Controllers 530 and 580 furthercontrol the operation of various processing units at the access pointand user terminal, respectively. Memory units 532 and 582 store data andprogram codes used by controllers 530 and 580, respectively.

FIG. 6 shows a block diagram of the spatial processing performed byaccess point 210 x and user terminal 220 x to transmit data on multipleeigenmodes on the downlink and uplink.

On the downlink, within TX spatial processor 520 at access point 210 x,the data vector s_(dn)(k) for each subband k is first multiplied withthe matrix Ũ_(ap)*(k) by a unit 610 and further multiplied with thecorrection matrix {circumflex over (K)}_(ap)(k) by a unit 612 to obtainthe transmit vector x_(dn)(k) for subband k. The columns of the matrixŨ_(ap)*(k) are orthogonalized as described above. The transmit vectorsx_(dn)(k), for k∈K, are then processed by a transmit chain 614 withinmodulator 522 and transmitted over the MIMO channel to user terminal 220x. Unit 610 performs the spatial processing for downlink datatransmission.

At user terminal 220 x, the downlink modulated signals are processed bya receive chain 654 within demodulator 554 to obtain the receive vectorsr_(dn)(k), for k∈K. Within RX spatial processor 560, the receive vectorr_(dn)(k) for each subband k is first multiplied with the matched filtermatrix {circumflex over (M)}_(ut)(k) by a unit 656 and furthermultiplied with the scaling matrix G_(ut)(k) by a unit 658 to obtain thevector ŝ_(dn)(k), which is an estimate of the data vector s_(dn)(k)transmitted for subband k. Units 656 and 658 perform the downlinkmatched filtering.

On the uplink, within TX spatial processor 590 at user terminal 220 x,the data vector s_(up)(k) for each subband k is first multiplied withthe matrix {circumflex over (V)}_(ut)(k) by a unit 660 and then furthermultiplied with the correction matrix {circumflex over (K)}_(ut)(k) by aunit 662 to obtain the transmit vector x_(up)(k) for subband k. Thetransmit vectors x_(up)(k), for k∈K, are then processed by a transmitchain 664 within modulator 554 and transmitted over the MIMO channel toaccess point 210 x. Unit 660 performs the spatial processing for uplinkdata transmission.

At access point 210 x, the uplink modulated signals are processed by areceive chain 624 within demodulator 522 to obtain the receive vectorsr_(up)(k), for k∈K. Within RX spatial processor 540, the receive vectorr_(up)(k) for each subband k is first multiplied with the matched filtermatrix {tilde over (M)}_(ap)(k) by a unit 626 and further multiplied bythe scaling matrix G_(ap)(k) by a unit 628 to obtain the vectorŝ_(up)(k), which is an estimate of the data vector s_(up)(k) transmittedfor subband k. Units 626 and 628 perform the uplink matched filtering.

The techniques described herein to derive eigenvectors for spatialprocessing may be implemented by various means. For example, thesetechniques may be implemented in hardware, software, or a combinationthereof. For a hardware implementation, the elements used for thesetechniques may be implemented within one or more application specificintegrated circuits (ASICs), digital signal processors (DSPs), digitalsignal processing devices (DSPDs), programmable logic devices (PLDs),field programmable gate arrays (FPGAs), processors, controllers,micro-controllers, microprocessors, other electronic units designed toperform the functions described herein, or a combination thereof.

For a software implementation, the techniques may be implemented withmodules (e.g., procedures, functions, and so on) that perform thefunctions described herein. The software codes may be stored in a memoryunit (e.g., memory units 532 and 582 in FIG. 5) and executed by aprocessor (e.g., controllers 530 and 580). The memory unit may beimplemented within the processor or external to the processor, in whichcase it can be communicatively coupled to the processor via variousmeans as is known in the art.

Headings are included herein for reference and to aid in locatingcertain sections. These headings are not intended to limit the scope ofthe concepts described therein under, and these concepts may haveapplicability in other sections throughout the entire specification.

The previous description of the disclosed embodiments is provided toenable any person skilled in the art to make or use the presentinvention. Various modifications to these embodiments will be readilyapparent to those skilled in the art, and the generic principles definedherein may be applied to other embodiments without departing from thespirit or scope of the invention. Thus, the present invention is notintended to be limited to the embodiments shown herein but is to beaccorded the widest scope consistent with the principles and novelfeatures disclosed herein.

1. In a wireless multiple-input multiple-output (MIMO) communication system, a method of deriving a matched filter based on a steered reference, comprising: obtaining a plurality of sets of received symbols for the steered reference received via a first link and generated based on a plurality of steering vectors; and deriving the matched filter based on the plurality of sets of received symbols, wherein the matched filter includes a plurality of eigenvectors corresponding to the plurality of steering vectors.
 2. The method of claim 1, wherein each of the plurality of sets of received symbols is for a steered reference symbol generated based on one of the plurality of steering vectors.
 3. The method of claim 1, wherein the plurality of eigenvectors of the matched filter are orthogonal to one another.
 4. The method of claim 3, wherein the plurality of eigenvectors of the matched filter are orthogonalized using QR factorization.
 5. The method of claim 4, further comprising: estimating gains associated with the plurality of steering vectors based on the plurality of sets of received symbols; and ordering the plurality of eigenvectors based on the estimated gains.
 6. The method of claim 3, wherein the plurality of eigenvectors of the matched filter are orthogonalized using minimum square error computation.
 7. The method of claim 3, wherein the plurality of eigenvectors of the matched filter are orthogonalized using polar decomposition.
 8. The method of claim 1, wherein the steered reference is received over multiple frames.
 9. The method of claim 1, further comprising: performing matched filtering of a data transmission received via the first link using the matched filter.
 10. In a wireless multiple-input multiple-output (MIMO) communication system, a method of deriving eigenvectors used for spatial processing, comprising: obtaining a plurality of sets of received symbols for a steered reference received via a first link and generated based on a plurality of steering vectors, wherein each of the plurality of sets of received symbols is for a steered reference symbol generated based on one of the plurality of steering vectors; determining a plurality of scaled vectors based on the plurality of sets of received symbols, wherein each of the plurality of scaled vectors corresponds to a respective one of the plurality of steering vectors; and deriving a plurality of eigenvectors based on the plurality of scaled vectors, wherein the plurality of eigenvectors are used for matched filtering of data transmission received via the first link.
 11. The method of claim 10, wherein each of the plurality of scaled vectors is determined based on at least one set of received symbols for at least one steered reference symbol generated based on the corresponding steering vector.
 12. The method of claim 10, wherein the plurality of eigenvectors are orthogonal to one another.
 13. The method of claim 12, wherein the deriving includes performing QR factorization on the plurality of scaled vectors to obtain the plurality of eigenvectors.
 14. The method of claim 12, wherein the deriving includes performing polar decomposition on the plurality of scaled vectors to obtain the plurality of eigenvectors.
 15. The method of claim 12, wherein the deriving includes performing minimum square error computation on the plurality of scaled vectors to obtain the plurality of eigenvectors.
 16. The method of claim 12, further comprising: estimating singular values based on the plurality of scaled vectors; and deriving a matched filter for the first link based on the plurality of eigenvectors and the estimated singular values.
 17. The method of claim 12, wherein the plurality of eigenvectors are used for spatial processing for data transmission on a second link.
 18. The method of claim 17, wherein the first link is an uplink and the second link is a downlink in the MIMO communication system.
 19. The method of claim 12, wherein the MIMO communication system utilizes orthogonal frequency division multiplexing (OFDM), and wherein the plurality of eigenvectors are derived for each of a plurality of subbands.
 20. A memory communicatively coupled to a digital signal processing device (DSPD) capable of interpreting digital information to: determine a plurality of scaled vectors based on a plurality of sets of received symbols for a steered reference generated based on a plurality of steering vectors and received via a first link in a wireless multiple-input multiple-output (MIMO) communication system, wherein each of the plurality of scaled vectors corresponds to a respective one of the plurality of steering vectors; and derive a plurality of eigenvectors based on the plurality of scaled vectors, wherein the plurality of eigenvectors are suitable for use for spatial processing.
 21. An apparatus in a wireless multiple-input multiple-output (MIMO) communication system, comprising: a receive spatial processor operative to process a plurality of sets of received symbols for a steered reference to provide a plurality of scaled vectors, wherein the steered reference is received via a first link and generated based on a plurality of steering vectors, and wherein each of the plurality of scaled vectors corresponds to a respective one of the plurality of steering vectors; and a controller operative to derive a plurality of eigenvectors based on the plurality of scaled vectors, and wherein the receive spatial processor is further operative to perform matched filtering of a first data transmission received via the first link using the plurality of eigenvectors.
 22. The apparatus of claim 21, wherein the controller is further operative to estimate singular values based on the plurality of scaled vectors and to derive a matched filter for the first link based on the plurality of eigenvectors and the estimated singular values.
 23. The apparatus of claim 21, wherein the plurality of eigenvectors are orthogonal to one another.
 24. The apparatus of claim 23, wherein the controller is operative to perform QR factorization, polar decomposition, or minimum square error computation on the plurality of scaled vectors to obtain the plurality of eigenvectors.
 25. The apparatus of claim 21, further comprising: a TX spatial processor operative to perform spatial processing for a second data transmission on a second link using the plurality of eigenvectors.
 26. The apparatus of claim 21, wherein the MIMO communication system utilizes orthogonal frequency division multiplexing (OFDM), and wherein the plurality of eigenvectors are derived for each of a plurality of subbands.
 27. An apparatus in a wireless multiple-input multiple-output (MIMO) communication system, comprising: means for determining a plurality of scaled vectors based on a plurality of sets of received symbols for a steered reference received via a first link and generated based on a plurality of steering vectors, wherein each of the plurality of scaled vectors corresponds to a respective one of the plurality of steering vectors; and means for deriving a plurality of eigenvectors based on the plurality of scaled vectors, wherein the plurality of eigenvectors are suitable for use for spatial processing.
 28. The apparatus of claim 27, further comprising: means for performing matched filtering of a first data transmission received via the first link using the plurality of eigenvectors.
 29. The apparatus of claim 27, further comprising: means for performing spatial processing for a second data transmission on a second link using the plurality of eigenvectors.
 30. The apparatus of claim 27, wherein the plurality of eigenvectors are orthogonal to one another. 